OPERATORS ON HILBERT SPACE

by

John Erdos

King's College London

Notes on the basic theoretical development of Hilbert space operators with some exercises.

They are designed to be supplement by examples and applications.

The notes contain links, but they only work within the current section.

For the benefit of those who want to use the links, the notes in one continuous section can be accessed here.

Introduction

1. Elementary properties of Hilbert space.

2. Linear operators.

3. Orthonormal sets.

4. Compact operators.

5. The spectrum.

6. The spectral analysis of compact opertors.

7. The Sturm-Liouville problem.

8. The spectral analysis of selfadjoint operators.